Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

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• 作者：Rainer Buckdahn (1) (2)
  Dan Goreac (3)
  Marc Quincampoix (1)
  
• 关键词：Stochastic control ; Asymptotic value function ; Uniform?Abel ; Tauberian theorems ; Occupation measures
• 刊名：Applied Mathematics and Optimization
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：70
• 期：1
• 页码：1-28
• 全文大小：856 KB
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• 作者单位：Rainer Buckdahn (1) (2)
  Dan Goreac (3)
  Marc Quincampoix (1)
  
  1. Laboratoire de Mathématiques de Bretagne Atlantique (CNRS UMR 6205), Université de Brest, 6 Avenue Victor le Gorgeu, 29200, Brest, France
  2. School of Mathematics, Shandong University, 27 South Shanda Road, Jinan, Shandong, 250100, P.R. China
  3. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, 77454, Marne-la-Vallée, France
  
• ISSN：1432-0606

文摘

We consider an optimal stochastic control problem for which the payoff is the average of a given cost function. In a non ergodic setting, but under a suitable nonexpansivity condition, we obtain the existence of the limit value when the averaging parameter converges (namely the discount factor tends to zero for Abel mean or the horizon tends to infinity for the Cesàro mean). The main novelty of our result lies on the fact that this limit may depend on initial conditions of the control system (in contrast to what is usually obtained by other approaches). We also prove that the limit does not depend of the chosen average (Abel or Cesàro mean).